Lightlike hypersurfaces on a four-dimensional manifold endowed with a pseudoconformal structure of signature (2, 2)

1999/02/24 by Maks A. Akivis, Vladislav V. Goldberg
Mathematics · #math.DG #msc:53A30 #msc:53B25

paper · pdf

published as Atti Congr Intern in honour of Pasquale Calapso (Messina, 1998), Palermo, 2000, pp. 159-190 · LaTeX, 23 pages

arxiv created 1999/02/24 · arxiv updated 2009/11/30

Abstract

The authors study the geometry of lightlike hypersurfaces on a four-dimensional manifold (M, c) endowed with a pseudoconformal structure c = CO (2, 2). They prove that a lightlike hypersurface V ⊂ (M, c) bears a foliation formed by conformally invariant isotropic geodesics and two isotropic distributions tangent to these geodesics, and that these two distributions are integrable if and only if V is totally umbilical. The authors also indicate how, using singular points and singular submanifolds of a lightlike hypersurface V ⊂ (M, c), to construct an invariant normalization of V intrinsically connected with V.

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